I LOVE(D) the concept of Clothesline math, but not so much the “logistics.” If your whiteboard is magnetic, cards and magnets, with a long line drawn on the board is a possible alternative. ☺️
(Retired … hence the “loved” 🤷♀️)
10% of 300 is 30, so 5% of 300 is half of that, or 15.
To find 95%, take 5% away from the whole thing: 300-15=300-10-5=285
LOVE this!!!
Here’s a link to an interactive Geogebra applet by Matthew Ziegler that I ran across YEARS ago that demonstrates this graphical approach ☺️
www.geogebra.org/m/QHgYSXT4
I do agree there must be some resisters working in puzzles … case in point:
Strands #567
“Stand by me”
🟡🔵🔵🔵
🔵🔵
🤷♀️🤞☺️
14/40 is equivalent to 7/20, and since 20 is a friendly factor of 100, I can easily find ANOTHER equivalent fraction: 35/100, which is the same as 35% ☺️
It would be interesting to see the data for the next seven years. While climate change has influenced increasingly occurring climate-related crises, simultaneously, the “climate change hoax” propaganda has ramped up considerably.
Would both blue and red be on an upward trend? 🤔🤷♀️
Thanks! ☺️
🎉🎉🎉☺️
I know it’s the next day, but these were lovely prompts!
I am always an advocate of making connections within a concept as well as between concepts to develop deeper understanding!
Focus on …
4x9x2 is 4 groups of 9x2 (as in the original 4x18) …
or 2 groups of 4x9
(Or even 9 groups of 4x2)
Investigate how to break up that big block of 4x18 into smaller pieces 🤔🤔🤔
And then … “oh, these are all ways to decompose 12”
How can we write that?
5x12=5x(6+6)
or 5x(10+2), etc
(Of course, I am also a strong advocate of area models for seeing these connections … big block of 5 by 12 … how can we break it into smaller pieces … how can we represent those pieces)
I think introducing parentheses too early confuses students - they think “do parentheses first” from Order of Operations.
It’s important for them to notice, for instance, the equivalence of:
5x12 and 5x6+5x6
or …
5x12 and 5x10+5x2
or …
5x12 and 5x8+5x4
even the “less friendly”
5x12 and 5x9+ 5x3
Cindy Whitehead
Retired HS / MS math teacher
PNW
My daughter came to visit for Easter! ☺️
This is like a “fact family” extension!
5x26
5x(20 +6)
5x20 + 5x6
100 + 30
130
It’s the “partner” to the division!
The concepts of “place value” and “like terms”!
50 + 30 is 80 … similarly, you can “add the 5 and 3” only because they represent 5 tens and 3 tens.
5x + 3x = 8x because there are
“5 x’s and 3 x’s”
So important for Elem/Secondary teachers to be more aware of what can be /has been done in Elementary that can support deeper understanding and connections to what is learned in secondary!!
COMMUNICATION!
I notice that blue and black “start with the big numbers”
I wonder if students are done a disservice by always focusing on “starting with the ones”
If students “always” go to the typical:
(20+7)(30+3) it becomes almost as rote as the traditional algorithm… 🤔🤔🤔
I like that I can mentally calculate 33x3, but not 33x7 … but 27 is 3 less than 30, so …
(30-3)x33 is
30x33 - 3x33
990 - 99
990 - 90 - 9
900 - 9
891
I like breaking 126 into 125 + 1.
8x125 is 1000
(2x125=250, and 4 of those is 1000, but also 1/8=0.125, sticks in my head)
Then there’s just one more 8, so 1008
I like the purple one for students who might be less fluent with “multiplication facts.”
Breaking one factor into “more parts” might seem like “more work,” but not if they are “friendlier pieces.”
Don’t parents teach kids what words mean all the time? “Ball” while holding a ball, etc.
Are you implying that kids “know where the vowel goes” and “knows how clauses work” by age five? Aren’t those concepts learned at school?
“Hanging out listening to them talk about math” is not what I meant by a mathematically rich environment. Playing with patterns, shapes, and number concepts with a child can provide the same foundation for learning math that verbal interactions provide for language development.
Babies don’t learn language just by “being in the world.” If they are not spoken to / interacted with on a regular basis, their language acquisition by age five would be very minimal. On the other hand, a child who grows up in a mathematically rich environment will be quite fluent by age five.
Trying to avoid spoilers …
What do the hens “do” ? 🤔🤔🤔
Make it friendlier …
104 - 44 …
104 - 4 = 100, then
100 - 40 = 60
But since it was really only 103, the result is one less, so 59
Each step adds one more row of 3 to the bottom, and an extra “one more flower” on the top.
Step 4 would have 4 rows of 3 flowers as well as just 3 “sticking out of the top” (4x3+3)
Step 25 would have 25 rows of 3 flowers and 24 more flowers sticking up at the top.” (25x3 + 24)
I think of 45° angles … 8 45’s makes an entire revolution … 360☺️
Image of a map of the Gulf of MEXICO from MapQuest
Or not … 😔
Hang in there MapQuest 👍🤞
(As well as WIKIPEDIA!!!)
Picture from Apple Maps showing Gulf of Mexico
At least there’s still this🤷♀️
Start with only 15 x 24 … half and double …
30 x 12 =360, then add on the last 24 … 384